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Confusion regarding input data set/series for ARIMA model

We are trying to predict electric motor failures/maintenance,so started reading about ARIMA model for predictions.
In every example i noticed data series consists of independent observations at different points of time. Eg temperature series / sale numbers / stock prices etc etc, so the data series looks like as follows:
Time1 : Value1
Time2 : Value2
Time3 : Value3
.. and so on …